Statistics for Decision Making: Case Study — Mutual Funds to write analysis report Essay Example
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Statistics for Decision Making
Case Study: Mutual Funds
Table of Contents
1.0 Introduction 4
1.1 Objectives 4
2.0 Business problem 4
4.0 Data analysis and interpretation 6
Shares categories Analysis 6 1.1
Performance of Assets based on growth risk 9 1.2
Growth and value analysis 11 1.3
Quarter and yearinterval performance 13 1.4
Expense ratio for shares 14 1.5
Assets recorded by the shares categories 15 1.6
Mutual funds and fees payment 17 1.7
4.9 Performance during the worst quarter 17 1.8
Inferential Statistics 18 1.9
TTests for 2013 Returns 18 1.9.1
6.0 General Conclusion 23
7.0 Implications 23
7.0 Bibliography 24
Executive Summary
This report presents a case study where the investment analyst conducts an analysis to guide clients regarding investment decision on available mutual funds. SPSS (Statistical Package for Social Scientists) software was used for data entry and statistical analysis. The analyzed variables included: category of shares (small cap, mid cap, large cap); objective – objective of shares comprising the mutual fund–growth or value; assets, fees; expenses ratio; return; risk; best quarter and worst quarter. The performance variables (Expense ratio, 3 year return, 5 year Return and return 2013) were analyzed basing on funds characteristics (Category, Objectives, Risk and Fees). According to the statistical results’ analysis, small cap shares are the best option to consider in share investment plans of the company and individuals, followed by the large cap shares, basing on different characteristics; this information will be availed to the client for them to select among large cap, mid cap and small cap stocks. However, during recession the easier option to venture into is mid cap. In conclusion, the report recommends that the most reasonable investment choice for clients is small cap shares as per the statistical analysis.
Statistics for DecisionMaking: Analysis report of case studymutual funds
1.0 Introduction
Mutual fund is defined as the type of trust by a sponsor where trustees raise money using the sale of units to the public, using various schemes, in order to invest in securities according to the regulations (Gadhi & Perumal, 2016. This report presents a case study where the investment analyst for clients is required to make an analysis for clients. After the analysis, the investment analyst is required to provide guidelines for the clients to make reasonable decisions among the available mutual funds for their retirement account.
1.1 Objectives

To provide general guidelines for clients to select a fund based on different characteristics

To guide client to make a reasonable choice among the many funds available
2.0 Business problem
In the current business world, there are numerous investment choices and mutual fund is booming sector that provides an opportunity for investors to generate income and returns (Joshi, 2013). The business problem in the case study involves making a decision to buy mutual funds for investors’ retirement account. Accordingly, the investment analyst is required to make analysis and reach the most suitable decision for clients purchasing mutual funds for their retirement account.
3.0 Methodology
SPSS (Statistical Package for Social Scientists) software was used for data entry and statistical analysis. Descriptive statistics were used to provide an overview of the data. Pearson’s correlation test was used to measure the strength of the association and relationship between the variables. Regression analysis was used to determine overall fit and relative contribution of variables and all predictors.
4.0 Data analysis and interpretation

Shares categories Analysis
Data was collected to understand share categories and their respective performance. Analyses are conducted based on frequencies and other descriptive statistics.
Small Caps Performance
Return 2013 
5YrReturn 
3YrReturn 

48.38333 
12.71667 
15.69167 

Standard Error 
1.461605 
Standard Error 
Standard Error 
0.713055 

Standard Deviation 
11.32154 
Standard Deviation 
9.227302 
Standard Deviation 
5.523303 
Sample Variance 
128.1773 
Sample Variance 
85.14311 
Sample Variance 
30.50688 
Kurtosis 
0.89565 
Kurtosis 
0.58244 
Kurtosis 
1.002631 
Skewness 
Skewness 
0.26428 
Skewness 
0.39395 

From the category analysis of descriptive statistics, small cap category, 2013 returnspresented the highest number of shares (mean of 48.38333) followed closely by 3year return of 15.69167 shares by mean and finally the 5year return whose mean was 12.71 shares. This shows that smaller cap mutual funds are preferred on short term than on long term basis.
Figure 1: small cap mean share returns
The data below shows the mid cap category returns.
Return 2013 
5YrReturn 
3YrReturn 

46.19474 
6.210526 
15.01579 

Standard Error 
2.996669 
Standard Error 
2.059494 
Standard Error 
1.050404 
Standard Deviation 
13.06218 
Standard Deviation 
8.977125 
Standard Deviation 
4.578605 
Sample Variance 
170.6205 
Sample Variance 
80.58877 
Sample Variance 
20.96363 
Kurtosis 
0.409484 
Kurtosis 
0.72936 
Kurtosis 
0.194173 
Skewness 
0.724428 
Skewness 
0.178491 
Skewness 
0.31391 
From the descriptive statistics in the mid cap category, 2013 returns presented the highest number of shares (mean of 46.19474 slightly lower than in the small cap) followed by 3year return, which was almost equal to that of small cap of 15.01579shares by mean and finally the 5year return whose mean was 6.210526 shares, equal to half of the small cap shares in the same period. This shows that more mid cap mutual funds are equally preferred on short term than on long term basis.
Large cap
Return 2013 
5YrReturn 
3YrReturn 

32.77381 
1.342857 
7.097619 

Standard Error 
Standard Error 
0.974537 
Standard Error 
0.616832 

Standard Deviation 
9.178609 
Standard Deviation 
6.315723 
Standard Deviation 
3.997529 
Sample Variance 
84.24686 
Sample Variance 
39.88836 
Sample Variance 
15.98024 
Kurtosis 
0.33242 
Kurtosis 
0.63201 
Kurtosis 

Skewness 
0.164818 
Skewness 
0.395427 
Skewness 
0.572324 
From the statistics table in the large cap category, 2013 returns also presented the highest number of shares with a mean of 32.77381 followed by 3year return, which was less than half of mid cap of 7.0976 shares by mean and finally the 5year return whose mean was lowest at 1.342857 shares. The data implies a decrease in returns as the return period increases which means that mutual funds are preferred on short term than on long term basis.

Performance of Assets based on growth risk
The table below illustrates data about Performance of mutual fundsbased on various periods of risk.
Table 1: Mean Performance of mutual funds based on risk
Return 2013 
5YrReturn 
3YrReturn 

41.36207 
12.36552 
13.15517 

Standard Error 
1.631596 
Standard Error 
1.136944 
Standard Error 
0.765085 
Standard Deviation 
12.42586 
Standard Deviation 
8.658705 
Standard Deviation 
5.826713 
Sample Variance 
Sample Variance 
74.97318 
Sample Variance 
33.95059 

Kurtosis 
0.09275 
Kurtosis 
0.99646 
Kurtosis 
0.68865 
Skewness 
0.358427 
Skewness 
0.129869 
Skewness 

As shown in the table above, the total sum of assets of mutual funds at low risk category was higher in 2013 returns at 2399 than in 3year return period whose total was 763 and 5year return whose sum was smallest at 717.2 or a mean of 12.36.
The table below is a summary of sum and variation of mutual funds at different levels of risk for comparison
Risk level 
2013 return 
5YrReturn 
3YrReturn 

Sample variation 
Sample variation 
Sample variation 

74.97318 
33.95059 

65.51011 
41.87822 

High risk 
165.2606 
104.0426 
58.01904 
For 2013 returns, the sum of fixed assets of mutual funds dropped as risk increased. Returns were lower during high risk, and highest at low risk. The same trend was replicated for 3year and 5year return periods implying risk level influences the rate of return of mutual funds. This is shown in the figure below.
Figure 3: Total assets of shares categories against risk level
It is evident from the bar chart that the shares categories at low risk recorded the highest total sum of asset while the shares categories at high risk recorded the lowest return on investment.

Growth and value analysis
The growth patterns for the mutual funds were assessed as per the descriptive statistics shown below.
Return 2013 
5YrReturn 
3YrReturn 

40.85306 
2.520408 
11.09592 

Standard Error 
1.807517 
Standard Error 
1.310949 
Standard Error 
1.017537 
Standard Deviation 
12.65262 
Standard Deviation 
9.176646 
Standard Deviation 
7.122762 
Sample Variance 
160.0888 
Sample Variance 
84.21082 
Sample Variance 
50.73373 
Kurtosis 
0.41473 
Kurtosis 
0.565568 
Kurtosis 
0.59167 
Skewness 
0.321378 
Skewness 
1.000092 
Skewness 
0.385748 
By mean, the growth pattern was generally low other than in the 2013 return period. The long term 5year return period specifically performed very poorly recording the lowest mean of 2.520408 shares. By sum, 2013 had the highest sum of shares (2001.8), followed by 3year return period with about a quarter the value of 2013 period and the lowest sum being for the 5year return period with 123.5 shares.Value was estimated as shown by the descriptive statistics below.
Return 2013 
5YrReturn 
3YrReturn 

11.30417 
13.62778 

Standard Error 
1.560812 
Standard Error 
Standard Error 
0.650975 

Standard Deviation 
13.24393 
Standard Deviation 
8.447859 
Standard Deviation 
5.523706 
Sample Variance 
175.4016 
Sample Variance 
71.36632 
Sample Variance 
30.51133 
Kurtosis 
0.20505 
Kurtosis 
0.84726 
Kurtosis 
0.43593 
Skewness 
0.358646 
Skewness 
0.111954 
Skewness 
0.10369 
Using mean as a standard measure of value, 2013 return period had the best value of 43.825 followed by 3year return period with 13.62 than 5year return period with 11.30.

Quarter and yearinterval performance
The survey aimed at determining the best quarter performance as well as year interval performance. Results were as displayed in the table below.
Category 

large cap 
Sum of Best Quarter 

Sum of 3YearReturn 

Sum of 5YearReturn 

Sum of Best Quarter 

Sum of 3YearReturn 

Sum of 5YearReturn 

small cap 
Sum of Best Quarter 

Sum of 3YearReturn 

Sum of 5YearReturn 

Total Sum of Best Quarter 

Total Sum of 3YearReturn 

Total Sum of 5YearReturn 
The small cap shares category recorded the highest sum of best quarter return whose value was 1915.5 followed closely by large cap shares category (1001.9). Mid cap shares category recorded the least return during its best quarter (580.6) compared to the large cap shares category and the small cap shares category. All the three categories recorded lowest returns after 5 years with small cap shares category recording 763, mid cap shares category 118 while large cap recording slightly lower than mid cap (56.4).
Moreover, the small cap shares category recorded more returns in their 3^{rd} year (941.5) than the one they recorded during the 5^{th} year (763). The same results were displayed by the large cap shares category that recorded 298.1 in their 3^{rd} year and 56.4 in their 5^{th} year. Similarly, mid cap share category displayed the same trend of results recording 285.3 in their 3^{rd} year and 118 in their 5^{th} year.
The results in this section imply that returns on shares invested reduced as time increased whose implication was a reduction the capital investments.

Expense ratio for shares
The sum of expense ratio for shares categories at low risk was higher (79.92) followed by the sum of expense ratios for average risk shares categories (58.9) while those at high risk recorded the least sum of expense ratio (24.3). This indicates that mutual fund types associated with high risks incur expenditure less than mutual funds with low risks.
Analysis of Expense ratio at various types of mutual funds
Table 5: Expense ratio at various types of mutual funds
Category 
Total Expense ratio 
Large Cap 

Small Cap 

Grand Total 
The total of expense ratio also varies with the type of mutual funds type.
Figure 2: Expense ratio at various types of mutual funds
As indicated in the figure above, the small cap mutual funds category recorded the highest sum of expense ratio (85.53).The large cap mutual funds category followed closely with 51.73. The mid cap mutual funds category recorded the lowest sum of expense ratio which was 25.69. This shows that the small cap share category spends more than the other types of mutual funds.

Assets recorded by the shares categories
The table below shows the sum of assets recorded by the shares categories against the risk level.
Table 3: Sum of Assets
111952.5 

142743.9 

Grand Total 
286290.8 
The shares category with low risk had the highest sum of assets (142743.9) followed by the shares category with average risk (111952.5) and shares category with high risk recorded the least sum of assets (31594.4). This indicates that the mutual fund types with low risks performed better than those with high risks.
Figure 4: A Pie Chart Showing Shares Categories and Their 2013 Return
Small cap shares category recorded the highest percentage of returns in 2013 followed by large cap shares category. Mid cap shares category recorded the least returns in the year 2013. Small cap shares are therefore the best option to consider in share investment plans of the company and individuals.

Mutual funds and fees payment
97 of the mutual funds categories do not pay fees while the remaining 24 pay fees as shown below.
Figure 5: Line graph of mutual funds types against fees payment

4.9 Performance during the worst quarter
Another aspect of the study was finding out the performance of the mutual funds types during their worst quarter.
Table 4: The performance of the mutual funds types during their worst quarter
Category 

large cap 

small cap 

Grand Total 
The performance of the small cap mutual funds type was the worst recording a deficit of 1131.5. The performance of the large cap mutual funds type followed with a deficit of 736.8 while the mid cap mutual funds type recorded an average deficit of 366.6 during their worst quarter. This shows that during recession the easier option to venture into is mid cap for such periods.

Inferential Statistics

TTests for 2013 Returns

Statistical tests were carried out to test 2013 returns. The H_{1}is that mutual funds will be more viable when invested on short term basis. The null hypothesis (H_{0}) is that mutual funds will be not be more viable when invested on short term basis.
SeparateVariances T Test for the Difference Between Two Means
(Assumes unequal population variances)
Hypothesized Difference 
0 
Level of Significance 

Population 1 Sample 

Sample Size 

Sample Mean 
42.60515464 
Sample Standard Deviation 

Population 2 Sample 

Sample Size 

Sample Mean 

Sample Standard Deviation 

Intermediate Calculations 

Numerator of Degrees of Freedom 

Denominator of Degrees of Freedom 

Total Degrees of Freedom 

Degrees of Freedom 

Standard Error 

Difference in Sample Means 
0.082345361 
SeparateVariance t Test Statistic 

LowerTail Test 

Lower Critical Value 

Do not reject the null hypothesis 
At 0.05 significant level, the decision rule is: Reject H_{0} if Tstat<1.6820 or Tstat> 0.4876.Do not reject H_{0} if 1.6820 ≤Tstat≤ 0.4876. The t statistic is 0.0313 which is within the range of 1.6820 ≤Tstat≤ 0.4876 hence the null hypothesis is not rejected implying that there is no enough evidence to show that short term investment of mutual funds is most viable.
SeparateVariances t Test for the Difference Between Two Means 

(assumes unequal population variances) 

Hypothesized Difference 
0 

Level of Significance 

Population 1 Sample 

Sample Size 

Sample Mean 
12.41340206 

Sample Standard Deviation 

Population 2 Sample 

Sample Size 

Sample Mean 
13.36666667 

Sample Standard Deviation 

Intermediate Calculations 
Calculations Area 

Numerator of Degrees of Freedom 
Pop. 1 Sample Variance 

Denominator of Degrees of Freedom 
Pop. 2 Sample Variance 

Total Degrees of Freedom 
Pop. 1 Sample Var./Sample Size 

Degrees of Freedom 
Pop. 2 Sample Var./Sample Size 

Standard Error 
For onetailed tests: 

Difference in Sample Means 
0.953264605 
TDIST value 

SeparateVariance t Test Statistic 
1TDIST value 

LowerTail Test 

Lower Critical Value 

Do not reject the null hypothesis 
The tstatistic is 0.7260 which falls above the lower critical value and the below the pvalue. The implication is that the null hypothesis is not rejected.
Intermediate Calculations 

Numerator of Degrees of Freedom 

Denominator of Degrees of Freedom 

Total Degrees of Freedom 

Degrees of Freedom 

Standard Error 

Difference in Sample Means 
0.75725945 
SeparateVariance t Test Statistic 

LowerTail Test 

Lower Critical Value 

Do not reject the null hypothesis 
There was no sufficient evidence from the t statistic (0.3182) to prove that 5year returns are best for mutual fund investment.
Significance of average returns at different risk levels and time
This was estimated through ANOVA test. The 2013 return data in this case is shown in the table below
Anova: Single Factor 

Variance 

48.38333 
128.1773 

46.19474 
170.6205 

32.77381 
84.24686 

Source of Variation 

Between Groups 
3153.775 
26.41624 
3.31E10 

Within Groups 
14087.75 
119.3877 

In this data, it is hypothesized that Ho: µ1= µ2= µ3 and Ha claiming that at least one of the mean is different from the others at various risk levels. In this case µ1: average mutual fund shares at low risk,µ2: average risk and µ3: high risk. From the data, Fcrit=F0.05, 2, 118= 3.07309. in other words, Ho is rejected when Fcalc>3.07309 and not rejected when Fcalc ≤ 3.07309. From the ANOVA data, Fcalc =26.41624>3.07309.
At the 95% confidence interval, Ho is rejected because Fcalc =26.41624>3.07309. Therefore, there is significant difference of the average returns on mutual funds at low, average and high risk at the 2013 return period.
The values for 5yr returns
Anova: Single Factor 

Source of Variation 

Between Groups 
3249.257 
1624.629 
23.63981 
2.32E09 

Within Groups 
8109.464 
68.72427 

11358.72 
From the data, Fcalc (23.6398)>F crit (3.07309) meaning that the null hypothesis is rejected providing evidence that supports a significant difference in the average of mutual funds returns at various levels of risk in the 5year return period. Similar results are obtained for 3year return period where F (40.74342) >F crit (3.07309) an indicator that the null hypothesis is rejected an implication that there is a significant difference between the mean returns at low, average and high risk for the 5year period
6.0 General Conclusion
The best types of shares to invest in are the mutual funds in the small cap category. This is because the analysis indicates that the small cap category had the highest number of shares. The next recommended type of share is the large cap shares because this category closely followed the small cap category. The least recommendable type of share is the mid cap category because the analysis indicates that this type had the least shares. In regard to the performance of assets based on their growth, the small cam mutual fund type is the best objective in driving the business. In addition, in regard to the best quarter performance and yearinterval performance, the small cap shares category recorded the highest sum of best quarter return whose value was 1915.5 followed closely by large cap shares category (1001.9). Mid cap shares category recorded the least return during its best quarter (580.6) compared to the large cap shares category and the small cap shares category. From the analysis, small cap shares are therefore the best option to consider in share investment plans of the company and individuals.
7.0 Implications
The statistical analysis provides a comparative analysis of proportion of investments of funds invested in various kinds of stocks, namely large cap, mid cap and small cap stocks. In addition, statistical analysis of the portfolio is important in understanding the variability of returns from the mutual funds when compared to previous year. Provided that the statistical analysis the report recommends that the most reasonable investment choice for clients is small cap shares as per the statistical analysis.
7.0 Bibliography
Gadhi K & Perumal R, 2016, Performance of Selected Bank Mutual Fund Schemes Impact in Investors’ Decision Making, International Journal of Advanced Research in Management and Social Sciences, 5(3), pp:361370.
Jagongo A & Mutswenje V, 2014, A Survey of the Factors Influencing Investment Decisions: The Case of Individual Investors at the NSE, International Journal of Humanities and Social Science, 4(4), pp: 92102.
Joshi J, 2013, Mutual Funds: An investment option from investors’ point of view, IBMRD’sJournal of Management and Research, 2(1), pp: 124134.
Krishnan R & Booker D, 2002, Investors’ use of Analysts’ recommendations, Behavioral Research in Accounting, 14(1).
Mohit G & Navdeep A, 2009, Mutual Fund Portfolio Creation Using Industry Concentration, Tura: ICFAI University.